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Area Method to Find Condition for Co-Linearity

If a, b,c, d,...

Question

If (a, b), (c, d), (e, f) are the vertices of a triangle such that a, c, e are in GP with common ratio r and b, d, f are in GP with common ratio s, then the area of the triangle is

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Solution

The correct option is B
Here, c = ar, e = $a r^{2}$ , d = bs, f = $b s^{2}$
$∴ Δ$ (Area of triangle) $= \frac{1}{2} ∣ ∣ ∣ ∣ \begin{matrix} a & b & 1 c & d & 1 e & f & 1 \end{matrix} ∣ ∣ ∣ ∣ = \frac{1}{2} a b (s - r) (s - 1) (r - 1)$

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